Hi, Courtney13. I'm also a very experienced crocheter and a pretty new knitter.
Gauge and tension are very different in the crochet and knit worlds. As you (and I!) experienced, a tension which in crochet feels "just right" is "too tight" in knitting. You'll want to use a larger knitting needle and loosen up quite a bit before getting back to the gauge swatch for the gloves. In fact, it might be helpful to make a very loose neck scarf as a transition project between the crochet items you've made and the knit gloves you plan to make. (Too bad you didn't check gauge for the lace shawl, but it's not too late: just knit a 5"x5" square using the needles & yarn recommended, and see where you are relative to the desired gauge. The more data in, the better conclusion you can draw.)
I received this advice only a couple of weeks ago, if that tells you where I am in the "learn to knit" process. The way my hands interpreted knitting tension, it felt almost sloppy relative to crochet tension. And at that precise moment, my one-on-one mentor said, "That's right! Just like that!" to my utter disbelief.
So that's my suggestion: use a larger needle, maybe two or three sizes larger, and lay down maybe 7 or 8 inches' worth of stitches in your cast-on. Then knit in whatever pattern (garter? all knit sts) (stockinette? knit one row, purl the next; repeat) is easiest for you, disregarding the 4-inch gauge idea. What you (and I) are looking for is springy, bouncy yarn a couple of rows out from the needle.
Very s-t-r-e-t-c-h-y stuff.
Best wishes on learning to knit!